MinT - Information on Result #974511

Information on Result #974511

Linear OOA(5¹⁵⁰, 152, F₅, 3, 51) (dual of [(152, 3), 306, 52]-NRT-code), using OOA 2-folding based on linear OOA(5¹⁵⁰, 304, F₅, 2, 51) (dual of [(304, 2), 458, 52]-NRT-code), using

trace code [i] based on linear OOA(25⁷⁵, 152, F₂₅, 2, 51) (dual of [(152, 2), 229, 52]-NRT-code), using
- constructionÂ X applied to AG(2;F,242P) âŠ‚ AG(2;F,248P) [i] based on
  1. linear OOA(25⁷⁰, 147, F₂₅, 2, 51) (dual of [(147, 2), 224, 52]-NRT-code), using algebraic-geometric NRT-code AG(2;F,242P) [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OOA(25⁶⁴, 147, F₂₅, 2, 45) (dual of [(147, 2), 230, 46]-NRT-code), using algebraic-geometric NRT-code AG(2;F,248P) [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148 (see above)
  3. linear OOA(25⁵, 5, F₂₅, 2, 5) (dual of [(5, 2), 5, 6]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(25⁵, 25, F₂₅, 2, 5) (dual of [(25, 2), 45, 6]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;45,25) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.